The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
Hyperbolic Groups
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Following prior work, we first advocate for using hyperbolic spaces which provably model tree-like structures better than Euclidean geometry.”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
In the citing paper
“For instance, the Euclidean space R n for n ≥ 2 is not δ -hyperbolic for any δ ≥ 0 , while the Poincar´ e ball D n is log(1+ √ 2) -hyperbolic.”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
In the citing paper
“Theorem : For any δ > 0 , any δ -hyperbolic metric space ( X,d X ) and any set of points x 1 , ..., x n ∈ X , there exists a finite weighted tree ( T, d T ) and an embedding f : T → X such that for all i, j ,”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
In the citing paper
“This exponential growth property enables hyperbolic spaces to embed any weighted tree while almost preserving their metric 3 (Gromov, 1987; Bowditch, 2006; Sarkar, 2011).”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
Citations
Cites
Lyndon, R. C., & Schupp, P. E. (2001) · Classics in mathematics · doi:10.1007/978-3-642-61896-3 · Cited by 1,026
Gromov, M. (1983) · Journal of Differential Geometry · doi:10.4310/jdg/1214509283 · Cited by 946
Self-citationFree subgroups in linear groups
Tits, J. (1972) · Journal of Algebra · doi:10.1016/0021-8693(72)90058-0 · Cited by 825
Manifolds of Nonpositive Curvature
Ballmann, W., Gromov, M., & Schroeder, V. (1985) · Progress in mathematics · doi:10.1007/978-1-4684-9159-3 · Cited by 784
Self-citationKlingenberg, W. (1978) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-642-61881-9 · Cited by 500
Markov Partitions for Axiom A Diffeomorphisms
Bowen, R. (1970) · American Journal of Mathematics · doi:10.2307/2373370 · Cited by 484
Geometry and Topology of Manifolds
Boden, H. U., Hambleton, I., Nicas, A., & Park, B. (2005) · American Mathematical Society eBooks · doi:10.1090/fic/047 · Cited by 417
Valuations, Trees, and Degenerations of Hyperbolic Structures, I
Morgan, J. W., & Shalen, P. B. (1984) · Annals of Mathematics · doi:10.2307/1971082 · Cited by 340
Groups Generated by reflections and aspherical manifolds not covered by Euclidean space
Davis, M. W. (1983) · Annals of Mathematics · doi:10.2307/2007079 · Cited by 337
On the existence and irreducibility of certain series of representations
Kostant, B. (1969) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1969-12235-4 · Cited by 271
Research works printed but not linked: 14
- A.D. Alexandrov, A theorem on triangles in a metric space and some of its applications, Trudy Math. Inst. Steks. 38 (1951), 5–23.
- N. Bourbaki, XXXIV, Groups et algébres de Lie, Part 2, Hermann, Paris, 1968.
- Yu. Burago and V. Zalgaller, Geometric Inequalities, Egrebn. der Math., Springer-Verlag, to appear.
- A. Dress, Trees, extensions of metric spaces and the cohomological dimension of certain groups, Preprint, Bielefeld.
- W.J. Floyd, Group completions and Kleinian groups, Ph.D. Thesis, Princeton, 1978.
- M. Gromov, Hyperbolic manifolds, groups and actions, In. Riemannian surfaces and related topics, Ann. Math. Studies 97 (1981), 183–215.
- M. Gromov, Hyperbolic manifolds, Volume and bounded cohomology, Publ. Math. IHES 56 (1983), 213–307.
- M. Gromov, Hyperbolic manifolds, Infinite groups as geometric objects, Proc. ICM Waszawa, Vol 1 (1984), 385–391.
- D. Kazdan, On a connection between the dual space of a group with the structure of it’s closed subgroups, Funct. An. and Applications, 1:1 (1967), 71–74.
- R.C. Lyndon and P.E. Schupp, Combinatorial group theory, Springer-Verlag (1977).
- G. Margulis, The isometry of closed manifolds of constant negative curvature with the same fundamental group, Dokl. Ak. Nauk. SSSR 192 (1970), 736–737.
- P. Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symmetriques, preprint.
- D. Sullivan, Quasiconformal homeomorphisms and dynamics, II, Preprint IHES, 1982.
- J.L. Tits, On buildings and their applications, Proc. I.C.M. 1974, pp. 209–221, Vancouver.
Cited by
Sorted by citations
Items 601–700 of 1,002
Hyperbolicity in the corona and join of graphs
Carballosa, W., Rodríguez, J. M., & Sigarreta, J. M. (2014) · Aequationes Mathematicae · doi:10.1007/s00010-014-0324-0 · Cited by 14
Effective metastability for modified Halpern iterations in CAT(0) spaces
Schade, K., & Kohlenbach, U. (2012) · Fixed Point Theory and Applications · doi:10.1186/1687-1812-2012-191 · Cited by 14
Origin of Hyperbolicity in Brain-to-Brain Coordination Networks
Tadić, B., Andjelković, M., & Šuvakov, M. (2018) · Frontiers in Physics · doi:10.3389/fphy.2018.00007 · Cited by 14
Random walks, WPD actions, and the Cremona group
Maher, J., & Tiozzo, G. (2021) · Proceedings of the London Mathematical Society · doi:10.1112/plms.12394 · Cited by 14
Bounded Geometry and p-Harmonic Functions Under Uniformization and Hyperbolization
Björn, A., Björn, J., & Shanmugalingam, N. (2020) · Journal of Geometric Analysis · doi:10.1007/s12220-020-00477-0 · Cited by 14
Stable cubulations, bicombings, and barycenters
Durham, M. G., Minsky, Y. N., & Sisto, A. (2023) · Geometry & Topology · doi:10.2140/gt.2023.27.2383 · Cited by 14
Joint hyperbolic and Euclidean geometry contrastive graph neural networks
Xu, X., Pang, G., Wu, D., & Shang, M. (2022) · Information Sciences · doi:10.1016/j.ins.2022.07.060 · Cited by 14
W$$^*$$-Rigidity Paradigms for Embeddings of $$\hbox {II}_1$$ Factors
Popa, S., & Vaes, S. (2022) · Communications in Mathematical Physics · doi:10.1007/s00220-022-04446-2 · Cited by 14
Finite asymptotic dimension for CAT(0) cube complexes
Wright, N. (2012) · Geometry & Topology · doi:10.2140/gt.2012.16.527 · Cited by 14
Residual finiteness growths of virtually special groups
Bou-Rabee, K., Hagen, M. F., & Patel, P. (2014) · Mathematische Zeitschrift · doi:10.1007/s00209-014-1368-5 · Cited by 14
Horoball Hulls and Extents in Positive Definite Space
Fletcher, P. T., Moeller, J., Phillips, J. M., & Venkatasubramanian, S. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-22300-6_33 · Cited by 14
Coarse hyperbolicity and closed orbits for quasigeodesic flows
Frankel, S. (2018) · Annals of Mathematics · doi:10.4007/annals.2018.188.1.1 · Cited by 14
A combination theorem for Anosov subgroups
Dey, S., Kapovich, M., & Leeb, B. (2018) · Mathematische Zeitschrift · doi:10.1007/s00209-018-2208-9 · Cited by 14
Hausdorff dimension of limit sets for projective Anosov representations
Glorieux, O., Monclair, D., & Tholozan, N. (2023) · Journal de l’École polytechnique — Mathématiques · doi:10.5802/jep.241 · Cited by 14
Decision problems and profinite completions of groups
Bridson, M. R. (2010) · Journal of Algebra · doi:10.1016/j.jalgebra.2010.06.019 · Cited by 14
Strong symbolic dynamics for geodesic flows on CAT ( - 1 ) spaces and other metric Anosov flows
Constantine, D., Lafont, J., & Thompson, D. J. (2020) · Journal de l’École polytechnique — Mathématiques · doi:10.5802/jep.115 · Cited by 14
Juriaans, S. O., Passi, I. B. S., & Prasad, D. (2004) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-04-07578-1 · Cited by 14
Subgroup properties of fully residually free groups
Kapovich, I. (2001) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-01-02840-9 · Cited by 14
Algebraic ending laminations and quasiconvexity
Mj, M., & Rafi, K. (2018) · Algebraic & Geometric Topology · doi:10.2140/agt.2018.18.1883 · Cited by 14
Polynomial upper bounds for the Dehn function of R. Thompson's group F
(1998) · Journal of Group Theory · doi:10.1515/jgth.1998.012 · Cited by 14
On 2-Systoles of Hyperbolic 3-Manifolds
Belolipetsky, M. (2013) · Geometric and Functional Analysis · doi:10.1007/s00039-013-0223-x · Cited by 14
Doubles, Finiteness Properties of Groups, and Quadratic Isoperimetric Inequalities
Bridson, M. R. (1999) · Journal of Algebra · doi:10.1006/jabr.1998.7710 · Cited by 14
Commensurability and separability of quasiconvex subgroups
Haglund, F. (2006) · Algebraic & Geometric Topology · doi:10.2140/agt.2006.6.949 · Cited by 14
Atoroidal Surface Bundles Over Surfaces
Bowditch, B. H. (2009) · Geometric and Functional Analysis · doi:10.1007/s00039-009-0033-3 · Cited by 14
Random walks and Brownian motion on cubical complexes
Nye, T. M. W. (2019) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2019.06.013 · Cited by 14
Expansion complexes for finite subdivision rules. I
Cannon, J. W., Floyd, W., & Parry, W. (2006) · Conformal Geometry and Dynamics of the American Mathematical Society · doi:10.1090/s1088-4173-06-00126-3 · Cited by 14
Translation numbers in a Garside group are rational with uniformly bounded denominators
Lee, E.-K., & Lee, S. (2007) · Journal of Pure and Applied Algebra · doi:10.1016/j.jpaa.2007.04.003 · Cited by 14
Extensions and submonoids of automatic monoids
Silva, P. V., & Steinberg, B. (2002) · Theoretical Computer Science · doi:10.1016/s0304-3975(01)00390-5 · Cited by 14
Small overlap monoids II: Automatic structures and normal forms
Kambites, M. (2009) · Journal of Algebra · doi:10.1016/j.jalgebra.2008.12.028 · Cited by 14
Rewriting Systems, Finiteness Conditions, and Associated Functions
Pride, S. J., & Wang, J. (2000) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-1388-8_11 · Cited by 14
Braid groups of imprimitive complex reflection groups
Corran, R., Lee, E.-K., & Lee, S. (2015) · Journal of Algebra · doi:10.1016/j.jalgebra.2015.01.004 · Cited by 13
Patterson–Sullivan theory for Anosov subgroups
Dey, S., & Kapovich, M. (2022) · Transactions of the American Mathematical Society · doi:10.1090/tran/8713 · Cited by 13
Quasi‐isometric diversity of marked groups
Minasyan, A., Osin, D., & Witzel, S. (2021) · Journal of Topology · doi:10.1112/topo.12187 · Cited by 13
τ-Cluster morphism categories and picture groups
Hanson, E. J., & Igusa, K. (2021) · Communications in Algebra · doi:10.1080/00927872.2021.1921184 · Cited by 13
Acylindrical hyperbolicity of automorphism groups of infinitely ended groups
Genevois, A., & Horbez, C. (2021) · Journal of Topology · doi:10.1112/topo.12203 · Cited by 13
Uniform negative immersions and the coherence of one-relator groups
Louder, L., & Wilton, H. (2024) · Inventiones mathematicae · doi:10.1007/s00222-024-01246-4 · Cited by 13
Islam, M. (2025) · Geometry & Topology · doi:10.2140/gt.2025.29.1171 · Cited by 13
A quantitative version of the Morse lemma and quasi-isometries fixing the ideal boundary
Shchur, V. (2012) · Journal of Functional Analysis · doi:10.1016/j.jfa.2012.11.014 · Cited by 13
Pattern rigidity and the Hilbert–Smith conjecture
Mj, M. (2012) · Geometry & Topology · doi:10.2140/gt.2012.16.1205 · Cited by 13
Limit groups over partially commutative groups and group actions on real cubings
Casals‐Ruiz, M., & Kazachkov, I. (2015) · Geometry & Topology · doi:10.2140/gt.2015.19.725 · Cited by 13
Many projectively unique polytopes
Adiprasito, K., & Ziegler, G. M. (2014) · Inventiones mathematicae · doi:10.1007/s00222-014-0519-y · Cited by 13
Hausdorff dimension and dendritic limit sets
Bowditch, B. H. (2005) · Mathematische Annalen · doi:10.1007/s00208-005-0647-1 · Cited by 13
On the number of vertices of positively curved planar graphs
Oh, B.-G. (2017) · Discrete Mathematics · doi:10.1016/j.disc.2017.01.025 · Cited by 13
Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families
Groves, D., & Hull, M. (2019) · Transactions of the American Mathematical Society · doi:10.1090/tran/7789 · Cited by 13
Counting problems in graph products and relatively hyperbolic groups
Gekhtman, I., Taylor, S. J., & Tiozzo, G. (2020) · Israel Journal of Mathematics · doi:10.1007/s11856-020-2008-x · Cited by 13
Cross ratios and cubulations of hyperbolic groups
Beyrer, J., & Fioravanti, E. (2021) · Mathematische Annalen · doi:10.1007/s00208-021-02330-3 · Cited by 13
Fundamental groups of asymptotic cones
Erschler, A., & Osin, D. (2005) · Topology · doi:10.1016/j.top.2005.02.003 · Cited by 13
A Bożejko–Picardello type inequality for finite-dimensional CAT(0) cube complexes
Mizuta, N. (2007) · Journal of Functional Analysis · doi:10.1016/j.jfa.2007.11.006 · Cited by 13
Quasi-isometries and isoperimetric inequalities in planar domains
Cantón, A., Granados, A., Portilla, A., & Rodríguez, J. M. (2015) · Journal of the Mathematical Society of Japan · doi:10.2969/jmsj/06710127 · Cited by 13
Cain, A. J., Gray, R. D., & Malheiro, A. (2018) · Journal of Combinatorial Theory Series A · doi:10.1016/j.jcta.2018.11.010 · Cited by 13
Invariant measures for the stable foliation on negatively curved periodic manifolds
Ledrappier, F. (2008) · Annales de l’institut Fourier · doi:10.5802/aif.2345 · Cited by 13
Product set growth in groups and hyperbolic geometry
Delzant, T., & Steenbock, M. (2020) · Journal of Topology · doi:10.1112/topo.12156 · Cited by 13
Virtual homological spectral radii for automorphisms of surfaces
Liu, Y. (2020) · Journal of the American Mathematical Society · doi:10.1090/jams/949 · Cited by 13
Kazhdan Constants of Hyperbolic Groups
Osin, D. (2002) · Functional Analysis and Its Applications · doi:10.1023/a:1021761810280 · Cited by 13
A Category of Noncrossing Partitions
Igusa, K. (2025) · Applied Categorical Structures · doi:10.1007/s10485-025-09838-8 · Cited by 13
Preservation and distortion of area in finitely presented groups
Gersten, S. M. (1996) · Geometric and Functional Analysis · doi:10.1007/bf02247889 · Cited by 13
Noncommutative rational functions and boundary links
Färber, M. (1992) · Mathematische Annalen · doi:10.1007/bf01444734 · Cited by 13
Conjugacy of 2-spherical subgroups of Coxeter groups and parallel wallsPreprint
Caprace, P. (2006) · Cited by 13
THE METRIC SPACE OF GEODESIC LAMINATIONS On A Surface IPreprint
Zhu, X., & Bonahon, F. (2003) · Cited by 13
SpaceMesh: A Continuous Representation for Learning Manifold Surface Meshes
Shen, T., Li, Z., Law, M. T., Atzmon, M., Fidler, S., Lucas, J., Gao, J., & Sharp, N. (2024) · SIGGRAPH Asia Conference Papers · doi:10.1145/3680528.3687634 · Cited by 12
On the hyperbolicity of bipartite graphs and intersection graphs
David Coudert, A., & Ducoffe, G. (2016) · Discrete Applied Mathematics · doi:10.1016/j.dam.2016.06.017 · Cited by 12
Gromov (non-)hyperbolicity of certain domains in ℂN
Николов, Н., Thomas, P. J., & Trybuła, M. (2015) · Forum Mathematicum · doi:10.1515/forum-2014-0113 · Cited by 12
When Can Graph Hyperbolicity Be Computed in Linear Time?
Fluschnik, T., Komusiewicz, C., Mertzios, G. B., Nichterlein, A., Niedermeier, R., & Talmon, N. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-62127-2_34 · Cited by 12
Configuration spaces of disks in an infinite strip
Alpert, H., Kahle, M., & MacPherson, R. (2021) · Journal of Applied and Computational Topology · doi:10.1007/s41468-021-00070-6 · Cited by 12
Growth of Quadratic Forms Under Anosov Subgroups
Carvajales, L. (2021) · International Mathematics Research Notices · doi:10.1093/imrn/rnab181 · Cited by 12
The dynamics and geometry of free group endomorphisms
Mutanguha, J. P. (2021) · Advances in Mathematics · doi:10.1016/j.aim.2021.107714 · Cited by 12
A topological zero-one law and elementary equivalence of finitely generated groups
Osin, D. (2020) · Annals of Pure and Applied Logic · doi:10.1016/j.apal.2020.102915 · Cited by 12
Discrete groups of packed, non-positively curved, Gromov hyperbolic metric spaces
Cavallucci, N., & Sambusetti, A. (2024) · Geometriae Dedicata · doi:10.1007/s10711-023-00874-z · Cited by 13
The Manhattan curve, ergodic theory of topological flows and rigidity
Cantrell, S., & Tanaka, R. (2025) · Geometry & Topology · doi:10.2140/gt.2025.29.1851 · Cited by 12
Total curvature and length estimate for curves in CAT(K) spaces
Maneesawarng, C., & Lenbury, Y. (2003) · Differential Geometry and its Applications · doi:10.1016/s0926-2245(03)00031-7 · Cited by 12
Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps
Belegradek, I. (2006) · Algebraic & Geometric Topology · doi:10.2140/agt.2006.6.1341 · Cited by 12
Boundaries of planar graphs: a unified approach
Hutchcroft, T., & Peres, Y. (2017) · Electronic Journal of Probability · doi:10.1214/17-ejp116 · Cited by 12
Data center interconnection networks are not hyperbolic
David Coudert, A., & Ducoffe, G. (2016) · Theoretical Computer Science · doi:10.1016/j.tcs.2016.05.025 · Cited by 15
Strongly singular MASAs and mixing actions in finite von Neumann algebras
Jolissaint, P., & STALDER, Y. (2008) · Ergodic Theory and Dynamical Systems · doi:10.1017/s0143385708000072 · Cited by 12
First passage percolation on a hyperbolic graph admits bi-infinite geodesics
Benjamini, I., & Tessera, R. (2017) · Electronic Communications in Probability · doi:10.1214/17-ecp44 · Cited by 12
The Deligne complex for the four-strand braid group
Charney, R. M. (2003) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-03-03425-1 · Cited by 12
On boundaries of hyperbolic Coxeter groups
Dranishnikov, A. N. (2001) · Topology and its Applications · doi:10.1016/s0166-8641(99)00172-8 · Cited by 12
Fujiwara, K. (2014) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-2014-06292-2 · Cited by 12
On discreteness of commensurators
Mj, M. (2011) · Geometry & Topology · doi:10.2140/gt.2011.15.331 · Cited by 12
GROUPS WITH QUADRATIC-NON-QUADRATIC DEHN FUNCTIONS
Olshanskii, A. Y. (2007) · International Journal of Algebra and Computation · doi:10.1142/s0218196707003688 · Cited by 12
On two conjectures of Maurer concerning basis graphs of matroids
Chalopin, J., Chepoi, V. D., & Osajda, D. (2015) · Journal of Combinatorial Theory Series B · doi:10.1016/j.jctb.2015.03.004 · Cited by 12
The Tits alternative for generalized tetrahedron groups
Howie, J., & Kopteva, N. (2006) · Journal of Group Theory · doi:10.1515/jgt.2006.012 · Cited by 12
On the Profinite Topology on Negatively Curved Groups
Gitik, R. (1999) · Journal of Algebra · doi:10.1006/jabr.1998.7847 · Cited by 12
Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs
Martínez-Pérez, Á., & Rodríguez, J. M. (2017) · Communications in Contemporary Mathematics · doi:10.1142/s021919971750050x · Cited by 12
On hyperbolic graphs induced by iterated function systems
Lau, K., & Wang, X. (2017) · Advances in Mathematics · doi:10.1016/j.aim.2017.04.012 · Cited by 12
Центральная предельная теорема на гиперболических группах
Benoist, Y., & Quint, J.-F. (2016) · Известия Российской академии наук Серия математическая · doi:10.4213/im8306 · Cited by 12
Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature II
Hua, B., & Jost, J. (2014) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-2014-06167-9 · Cited by 12
Crowley, K. D. (2008) · Geometriae Dedicata · doi:10.1007/s10711-008-9231-7 · Cited by 12
Existentially closed CSA-groups
Jaligot, É., & Houcine, A. O. (2004) · Journal of Algebra · doi:10.1016/j.jalgebra.2004.06.007 · Cited by 12
Homomorphism diagrams of surface groups
Olshanskii, A. Y. (1989) · Siberian Mathematical Journal · doi:10.1007/bf00970919 · Cited by 12
The metric space of geodesic laminations on a surface: I
Zhu, X., & Bonahon, F. (2004) · Geometry & Topology · doi:10.2140/gt.2004.8.539 · Cited by 12
Testing contractibility in planar rips complexes
Chambers, E. W., Erickson, J., & Worah, P. (2008) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/1377676.1377721 · Cited by 12
VERBAL SUBGROUPS OF HYPERBOLIC GROUPS HAVE INFINITE WIDTHPreprint
Myasnikov, A., & Nikolaev, A. (2016) · Cited by 12
Universal circles for quasigeodesic flowsPreprint
Calegari, D. (2004) · Cited by 12
Hyperbolic models for CAT(0) spaces
Petyt, H., Spriano, D., & Zalloum, A. (2024) · Advances in Mathematics · doi:10.1016/j.aim.2024.109742 · Cited by 11
Characterization of Gromov hyperbolic short graphs
Rodríguez, J. M. (2013) · Acta Mathematica Sinica English Series · doi:10.1007/s10114-013-2467-7 · Cited by 11
Rational growth in virtually abelian groups
Evetts, A. (2019) · Illinois Journal of Mathematics · doi:10.1215/00192082-8011497 · Cited by 11
Counting problems for special-orthogonal Anosov representations
Carvajales, L. (2020) · Annales de l’institut Fourier · doi:10.5802/aif.3333 · Cited by 11
Gelfert, K., & Ruggiero, R. O. (2023) · Annales de l’institut Fourier · doi:10.5802/aif.3574 · Cited by 11
Hoda, N. (2019) · The Michigan Mathematical Journal · doi:10.1307/mmj/1576832418 · Cited by 11
Metadata
- Authors
- Gromov, M.
- Corresponding author
- Gromov, M.
- Venue
- Mathematical Sciences Research Institute Publications
- Publisher
- Springer New York
- Published
- 1987
- Pages
- 75-263
- ISSN
- 0940-4740 (ISSN-L)
- OpenAlex
- W4235484205
- Cited by
- 1,817
- References
- 19
- Citations by year
- 2026: 41 · 2025: 106 · 2024: 94 · 2023: 92 · 2022: 87 · 2021: 90 · 2020: 72 · 2019: 69 · 2018: 72 · 2017: 82 · 2016: 79 · 2015: 75 · 2014: 68 · 2013: 66 · 2012: 54
- FWCI
- 19.75
- Type
- book chapter
- Language
- en
- Open access
- closed
- Locations
- Mathematical Sciences Research Institute publications (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Mathematics › Geometry and Topology › Mathematics and Applications
- Keywords
- hyperbolic groups, Gromov hyperbolicity, geometric group theory, Cayley graphs, word metric, hyperbolic geometry
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
